This invention relates to numerical control devices (hereinafter referred to as "NC devices", when applicable), and more particularly to an improvement of the accuracy in motion position of a movable part of a machine controlled by an NC device, such as a numerically controlled (NC) machine tool, which operates on a lost motion correction system in a semi-closed loop system which is one example of a servo loop system for a numerically controlled (NC) machine tool.
In a general semi-closed loop system for an NC machine tool, the torque of the servo motor is converted into a linear motion by a ball thread feed drive mechanism to linearly move a movable part of the NC machine tool, and in this operation, the position control of the movable part is carried out as follows: The position detection of the movable part is not made at its end; that is, the angle of rotation of the movable part is detected with a detector coupled to the end of the ball thread or the drive motor thereby to indirectly detect the position of the movable part. The feed drive mechanism is "twisted" or "bent" depending on a load applied thereto. Therefore, the stop position of the movable part when positioned in place in a forward (positive) direction will differ from that of the movable part when positioned in a reverse (negative) direction. In order to correct the difference between the two stop positions, a method has been employed in which the value with the feed speed set to about 100 mm/min, the difference is measured, and it is applied, as a backlash correcting value including a lost motion correcting value, to the NC device, to correct the amount of mechanical movement.
The lost motion, which is one of the factors causing the difference between the two stop positions, attributes to a mechanism different from the play (backlash) of the ball thread in the drive system. This will be described with reference to a linearly movable part such as a table, saddle or slide in a machine tool (hereinafter referred to as "a table", when applicable, for simplification in description) in brief.
FIG. 9 shows the arrangement of a general ball thread feed drive mechanism. The ball thread feed drive mechanism comprises a number of mechanical components such as a ball thread, bearings, brackets, and parts for mounting and securing these components. In the feed drive mechanism, various parts are displaced by a torque of the drive motor, and by the load of the system. The torque of the drive motor is transmitted through a coupling to the ball thread shaft to which tension has been given in advance to improve its rigidity, and to the nut section combined with the ball thread shaft, thus linearly driving the table which is fixedly secured to the nut section and is supported by linear bearings. On the other hand, in order to improve the rigidity and accuracy of the mechanical system, the bearing section supporting the ball thread shaft and the linear bearing section supporting the table are suitably pre-loaded, thus providing their best mechanical characteristics.
From these results, at the start of the movement of the table, the load torque to the servo motor is as indicated by the following equation (1): EQU M.sub.T0 .varies..mu..sub.0 .multidot.W.multidot.k.sub.1 +t.sub.NO +t.sub.MO +t.sub.BO +k.sub.2 .multidot.W.sub.I .multidot.f.sub.1.sup.2 +k.sub.3 .multidot.R.sub.I .multidot.f.sub.2.sup.2 +C (1)
where
M.sub.To : the torque to the servo motor at the start of the movement (load on the table=0)
.mu..sub.0 : the coefficient of friction of the table and the linear bearing section at the start of the movement
W: the weight of the table
k.sub.1 : the constant for converting linear motion force into torque
k.sub.2, k.sub.3 : the constants for converting inertial moment into torque
t.sub.N0 : the frictional torque of the ball thread shaft and the nut
t.sub.M0 : the servo motor frictional torque
t.sub.B0 : the frictional torque of the bearing section supporting the ball thread shaft
W.sub.I : the inertial moment of the table
R.sub.I : the inertial moment of the rotary section
f.sub.1 : the table speed
f.sub.2 : the speed of the rotary section
C: the constant
The friction affecting the torque is greatly changed by the pre-load, the viscosity and quantity of lubricant used, and the feed speed.
When a product weight w is applied onto the table, the load torque M.sub.Tw to the servo motor is as indicated by the following equation (2): EQU M.sub.Tw .varies..mu..sub.0 .multidot.(W+w).multidot.k.sub.1 +t.sub.NO +t.sub.MO +t.sub.B0 +k.sub.2 .multidot.(W.sub.I +w.sub.i).multidot.f.sub.1.sup.2 +k.sub.3 .multidot.R.sub.I .multidot.f.sub.2.sup.2 +C(2)
where
M.sub.Tw : the torque to the servo motor at the start of the movement (load on the table=W)
w.sub.I : the inertial moment of the product
The displacement in motion position of the table attributing to the torque depends on the displacement (elastic deformation) of the various parts, the ball thread, the ball thread shaft, the bracket section, and the stationary structure of the motor drive system. The twisting and bending of the ball thread shaft, being the function of the length between the drive section and the nut section, can be expressed as follows: EQU .DELTA.SM.sub.Tw .varies.k.sub.L .multidot..DELTA.S.sub.N .multidot.M.sub.Tw +.DELTA.S.sub.M .multidot.M.sub.Tw +.DELTA.S.sub.B .multidot.M.sub.Tw +.DELTA.S.multidot.S.sub.MTw +.DELTA.S.multidot.C (3)
where
.DELTA.SM.sub.Tw : the amount of displacement upon application of torque M.sub.Tw
.DELTA.S.sub.N .multidot.M.sub.Tw : the amount of displacement of the thread section upon application of torque M.sub.Tw
S.sub.M .multidot.M.sub.Tw : the amount of displacement of the motor section upon application of torque M.sub.Tw
.DELTA.S.sub.B .multidot.M.sub.Tw : the amount of displacement of the ball thread bearing and bracket section upon application of torque M.sub.Tw
.DELTA.S.multidot.SM.sub.Tw : the amount of displacement of the drive system stationary structure section upon application of torque M.sub.Tw
K.sub.L : the coefficient of displacement of the ball thread depending on the distance from the drive section
.DELTA.S.multidot.C: the constant
This displacement changes with the torque; that is, it changes when the speed of the table is increased from substantially zero (at rest) at around the speed of feed used for actual work, thus being proportional to the variations in the position of the table, the inertial moments of the moving parts, and the coefficients of frictions of the bearing sections and the table. The displacement mentioned above may be disregarded when the structure is made sufficiently rigid against the load. However, in the case where it is impossible to increase the rigidity because of the mechanical structure or manufacturing cost, sometimes those of the resultant machine are considerably large. In the case where the above-described table is positioned in the forward direction, and is moved in the opposite (reverse) direction, the torque is inverted in direction, and the table coupled through the ball thread to the servo motor will not be moved even if the servo motor rotates as much as the sum of the displacement in the forward direction and that in the reverse direction (two times the amount of displacement .DELTA.SM.sub.Tw). Thus, the amount of correction of baCklash, whiCh haS been initially measured and set with the speed of feed of about 100 mm/min, is not that which is determined by taking into account the speed of the feed, the load on the table, and the length of the ball thread from the drive section. Accordingly, the positioning effected under the conditions different from those preset is not sufficiently high in accuracy. With respect to the lost motion, if the servo motor is held at rest for a long time being firmly clamped, or the whole system is subjected to small oscillation, then the displacement may be released. FIG. 10 is a graphical representation indicating the follow-up characteristics of an NC machine tool. FIGS. 11 and 12 are also graphical representation generally indicating amounts of lost motion with speed of feed.
As is apparent from the above description, a conventional NC machine tool has the lost motion which changes essentially with machining conditions; however, it has no means for detecting only the lost motion. Accordingly, the NC device itself has no function of correcting the lost motion, and the correction has been performed in terms of backlash correction. Thus, whenever the machining conditions change, the machining accuracy is changed. Recently, there has been a strong demand for the provision of a stable and accurate machining technique, and accordingly for the correction of lost motion.